I do not think that it is a US/UK different usages, handy can also be used in American English, at least to my knowledge. Native speakers can provide you with clearer answers.
You could, but I'm not certain... Here in the U.S., both "come in useful" and "come in handy" are used, but the latter is far more common. The situation could be the opposite in the U.K., but I really couldn't say because I've never been there.